Comment on: The class of CUB models: statistical foundations, inferential issues and empirical evidence

  • Francesco BartolucciEmail author
  • Fulvia Pennoni

We congratulate with the authors for providing a very clear and comprehensive overview about Combination of Uniform and Binomial (CUB) models for the analysis of ordinal responses, in particular when these responses result from the formulation of ratings or preferences. We can testify that these models have successfully represented the main research interest of Professor Piccolo across the last 15 years at least; on this research field he has been able to involve many young researchers.

In the following, we provide comments on some relevant aspects of CUB models and on some topics that may represent certain possible developments, although we acknowledge the presence in the literature of a large number of already available extensions in several directions, which are well documented in the proposed article.

The heart of CUB models is the conceptualization of the selection process of a response category made by an individual among the possible item responses. An explanation of this...



  1. Bartolucci F, Colombi R, Forcina A (2007) An extended class of marginal link functions for modelling contingency tables by equality and inequality constraints. Stat Sin 17:691–711MathSciNetzbMATHGoogle Scholar
  2. Bartolucci F, Farcomeni A, Pennoni F (2013) Latent Markov models for longitudinal data. Chapman & Hall/CRC, Boca RatonzbMATHGoogle Scholar
  3. Bartolucci F, Bacci S, Gnaldi M (2015) Statistical analysis of questionnaires: A unified approach based on R and Stata. Chapman & Hall/CRC, Boca RatonCrossRefzbMATHGoogle Scholar
  4. Birnbaum A (1968) Some latent trait models and their use in inferring an examinee’s ability. In: Lord FM, Novick MR (eds) Statistical theories of mental test scores. Addison-Wesley, Reading, pp 395–479Google Scholar
  5. Hambleton RK, Swaminathan H (1985) Item response theory: Principles and applications. Kluwer Nijhoff, BostonCrossRefGoogle Scholar
  6. Krosnick JA (1991) Response strategies for coping with the cognitive demands of attitude measures in surveys. Appl Cogn Psychol 5:213–236CrossRefGoogle Scholar
  7. Krosnick JA (1999) Survey research. Annu Rev Psychol 50:537–567CrossRefGoogle Scholar
  8. Pennoni F (2016) Modelling a multivariate hidden Markov process on survey data. In: Proceedings of the 48th scientific meeting of the Italian Statistical Society, Università degli studi di Salerno, pp 1–10Google Scholar
  9. Tourangeau R, Rips L, Rasinski K (2000) The psychology of survey response. Cambridge University Press, CambridgeCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of PerugiaPerugiaItaly
  2. 2.Department of Statistics and Quantitive MethodsUniversity of Milano-BicoccaMilanItaly

Personalised recommendations